While preparing soft boiled eggs, I tested a variety of methods (including cooking the eggs in boiling water as the name suggests, bringing the water up to temperature while the eggs are in the water, holding the water at 150°F until the eggs are cooked, and steeping in just boiling water) in pots of different sizes. After deciding on the steeping method, I reran time tests to determine the best steeping time for a just peelable soft boiled egg. Here's the various stages of soft boiled eggs so you can choose the time that gives you the results you prefer.

Using the method described in Recipe File: Soft Boiled Eggs where the water is brought to a boil, pot moved off the heat source, refrigerated large eggs placed into the water, lid replaced, and eggs shocked in ice water after a set duration of time, I tested various amounts of time spent in the just boiling water.

After 2 minutes: The thin albumen (egg white closest to the shell) has turned white and is semi-solid but the thick albumen (egg white layer nearest to the yolk) is still clear and liquid.

After 3 minutes: The thin albumen has solidified. The thick albumen is liquid but turning white.

After 4 minutes: The thin albumen has fully solidified. The thick albumen is semi-solid.

After 5 minutes: The whites are solid, but when tilted they still flow.

After 6 minutes: The whites are solid but not stiff (moves a little when the egg is tilted). The yolk has begun to thicken, but the egg still can't be peeled intact.

After 7 minutes: The whites are solid but not stiff. The yolk has thickened but flows well.

After 8 minutes: The whites are solid. The yolk has thickened and parts are beginning to no longer flow.

After 9 minutes: The whites are solid. Half the yolk has gelled (solid but still translucent - not yet the opaque yellow of a hard boiled egg) and half continues to thickly flow.

Just repeat the test using the same procedure you've established on small and jumbo. Plot size (probably mass, but volume should work too) versus time and then interpolate/extrapolate to figure out the time you should use for the sizes you don't test.

I mean, it probably isn't a straight line given the fact that you have an egg cruising up in temperature to meet the water which is cooling down along a similar curve, and Newton's law of cooling implies that the curve supposed to be exponential, but it's shouldn't be too bad. What's the mass ratio between jumbo and the smallest size you're interested in? As long as it isn't 10 or so, I wouldn't worry about it. If it is, throw in one more size in between.

So wouldn't the amount of water in the pan along with the number of eggs contribute to the timing? A large amount would be more stable. Maybe an amount or water per egg would be the way to specify it.

What about the fridge internal temp? Or is somewhere around 38 fine?

It would be interesting to weigh various egg sizes from various sources to see if there is much variation.

Are the shells on brown eggs thicker? They seem to be for the ones I get and wouldn't that effect the timing as well?

In my experience, brown eggs to have stronger thicker shells, but not significantly where it would affect temperature rise in the yolk and albumen.

A volume of water per egg sounds good to me, and if we're real picky here, a pot with a water column equalling the diameter should result in the least amount of ambient heat loss.

Fridge temps should be fairly standard==about 35 to 37F. A couple of degrees should not make that much difference since the rate of heat absorption is greatest at the start of the heating cycle where the difference in temperature between the egg and water is the greatest.

I wonder how much elevation would matter -- would you need to do it longer at higher elevations?

Elevation would definitely make a difference since the temperature of the boiling water is lower than if you were at sea level. At 1,000 to 2,000 feet, the difference is small enough that you might not have to make adjustments but over 5,000 feet (where the water temperature is about 10 degrees F lower) you might need to add a minute or two.

I'm glad Liv asked about altitude. At 5,000 feet it does take me a little longer to achieve the same results.

(And if I plan to make spaghetti at 11,000 feet while camping, I boil the noodles most of the way at home and pack them in pre-cooked. You don't want to find out how long it takes to cook pasta at that altitude when you're really hungry.)

I would suggest re-running the test using freshly laid eggs i.e. those still warm from the laying process. A similar test could be run using eggs from the refrigerator. All of this has relevance because of the relative size of the air pocket within the shell and its expansion rate at the different temperatures